Are transformations of functions giving your students trouble? Try a covariation approach.

Consider this problem: Sketch a graph of a function y=f(x). Now sketch a graph of y=f(ax) for some constant value a>1. Reflect. What kind of graph did you sketch for y=f(x)? How did you decide what to sketch? Did you choose a particular value for a? How does your graph of y=f(ax) compare to your graph of y=f(x)? What is… Continue reading Are transformations of functions giving your students trouble? Try a covariation approach.

Graph Makeover: It’s about time

Think back to a time when you encountered a “real world” graph in a math class. What was on the horizontal axis? Probably TIME. Graphs represent relationships between two things. When working with graphs, it is important for students to form and interpret relationships between TWO things that can change. Yet, if one of those things is… Continue reading Graph Makeover: It’s about time

Use Tech to Broaden Students’ Opportunities for Math Reasoning

Subtitle: The reason I’m giving this talk at #NCTM2017. Our #NCTM2017 Online Playgrounds session is on Saturday, April 8 from 9:30-10:30 in Henry B. Gonzalez Convention Center, 214C@phornbein1 pic.twitter.com/27bFC3A2b7 — Heather Johnson (@HthrLynnJ) March 29, 2017 Think of technology as “playground equipment” that teachers can use to create online “learning playgrounds” for students. By using different… Continue reading Use Tech to Broaden Students’ Opportunities for Math Reasoning

Investigating Functions with a Ferris Wheel. Part 3: Exploring Distance and Width

Here are some tips for using the Ferris Wheel Distance-Width Interactive with students. The format is parallel to Investigating Functions with a Ferris Wheel: Part 2. I suggest using the Ferris Wheel Distance-Width Interactive after students have explored the Ferris Wheel Distance-Height Interactive. I introduced these interactives in Investigating Functions with a Ferris Wheel: Part 1. Explore changing distance and width: Ferris wheel animation Click Hide Width, Hide… Continue reading Investigating Functions with a Ferris Wheel. Part 3: Exploring Distance and Width

I study students’ mathematical reasoning, and I take real breaks.

Making time for leisure strengthens my scholarship. Leisure time is not a luxury, it is a necessity.#academiclife #PhD — Heather Johnson (@HthrLynnJ) March 17, 2017 This week I revisited an advice column, Workload Survival Guide for Academics, which I came across last year. Professor Andrew Oswald identified a price that comes along with the privilege of being… Continue reading I study students’ mathematical reasoning, and I take real breaks.

Investigating Functions with a Ferris Wheel. Part 2: Exploring Distance and Height

In Investigating Functions with a Ferris Wheel: Part 1 I shared two Web Interactives. Here are some tips to for using the Ferris Wheel Distance-Height Interactive with students. Explore changing distance and height: Ferris wheel animation Click Hide Height, Hide Distance, Hide Point, and Hide Trace. Press Animate Point. Questions for students: For a car beginning at start and moving once around the wheel,… Continue reading Investigating Functions with a Ferris Wheel. Part 2: Exploring Distance and Height

Investigating Functions with a Ferris Wheel: Part 1

Investigating Functions With A Ferris Wheel coauthored with Peter Hornbein (@phornbein1) and Sumbal Azeem, appeared in the December 2016/January 2017 issue of NCTM’s Mathematics Teacher journal. This winter, Max Ray-Riek (@maxmathforum) and Annie Fetter (@MFAnnie) converted my Geometer’s Sketchpad sketches into Web Sketchpad Activities, freely available through NCTM Illuminations: Investigating Functions with a Ferris Wheel: Distance vs.… Continue reading Investigating Functions with a Ferris Wheel: Part 1

Narrating students’ mathematical reasoning

Stories of “storytelling” have captured my interest this weekend: Storytelling is a vital human activity@SenorG https://t.co/CS3ql83ipu — Heather Johnson (@HthrLynnJ) February 25, 2017 “We need to tell different stories to expand our cultural understanding of who can engage in mathematics.”#mtbos #mathchat #math https://t.co/sKXpmAKmR5 — Heather Johnson (@HthrLynnJ) February 25, 2017 When I narrate students’ mathematical reasoning,… Continue reading Narrating students’ mathematical reasoning

Reaching a milestone, Allowing for introspection, Forging new possibilities

Reaching a milestone In 2016 I reached a milestone that I have been working toward for more than a decade. I earned tenure as a faculty member at a research intensive university. In 2005, when I shifted from high school classroom teacher to full time graduate student, I had only glimmers of notions of the journey that would… Continue reading Reaching a milestone, Allowing for introspection, Forging new possibilities